On solvability of a nonlinear problem in theory of income distribution. (English) Zbl 1258.45004

Khachatryan, A.; Khachatryan, Kh.

Eurasian Math. J. 2, No. 2, 75-88 (2011).

This paper considers a nonlinear integro-differential equation with a Hammerstein type noncompact operator, arising in the theory of income distribution. It proves the existence of a positive solution of the nonlinear problem in Sobolev space \(W_1^1(\mathbb R^+)\). Some examples arising in applications are shown. For one modeling problem a uniqueness theorem is proved. At the end of the paper the results of numerical calculations are given.

Reviewer: Li Xing (Yinchuan)

MSC:

45J05	Integro-ordinary differential equations
45G10	Other nonlinear integral equations
45M20	Positive solutions of integral equations
65R20	Numerical methods for integral equations

Keywords:

measurable function; iteration; factorization; density distribution; pointwise limit; mean income; numerical examples; integro-differential equation; Hammerstein type noncompact operator; income distribution; positive solution